But the much-anticipated public debut of the baby was under wraps. The infant was in her car seat, covered up by a white blanket as a nanny carried her from the parking garage into the doctor's Los Angeles office.

At one point, a smiling West, wearing a pair of $700 Trussardi "1911" fringe suede sneakers, stopped to tie a sweater around Kardashian's waist and take a large $20,000 Hermes leather bag she had been lugging.

Kanye West and Kim Kardashian were spotted taking their baby to the doctor on Wednesday. (SGGS/AKM-GSI)

"The bag is a gift from Kanye. He had it made for her," a source said. "It's her travel bag. She's using it for the baby."

West, 36, gave Kardashian the bag, with a gold-plated lock and goat-skin lining, at her baby shower.

The reality TV star gave birth June 14 at Cedars-Sinai Medical Center in Los Angeles. Baby North West — who's been nicknamed Nori — was born prematurely after her mother suffered pre-eclampsia, a condition marked by chronic high blood pressure.